A bigger circle centre at O and a smaller circle centre at P touch each other externally such that the length of their common tangent LM is 12 cm. If the radius of the bigger circle is 18 cm, then what will be the radius (in cm) of the smaller circle?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 2.
When two circles touch each other externally, the distance between their centers equals the sum of their radii. The length of the common tangent between two circles = √[(R + r)2 - (R - r)2]
Where R is the radius of the bigger circle and r is the radius of the smaller circle.
LM = 12 cm and OL (R) = 18 cm
Let, MP = r cm
So, √[(18 + r)2 - (18 - r)2] = 12
⇒ √(4 × 18 × r) = 12
⇒ √(72r) = 12
⇒ 6√(2r) 12
⇒ √(2r) = 2
⇒ 2r = 4
⇒ r = 4/2 = 2 cm
Therefore, the radius of the smaller circle is 2 cm.